Optimal (2,n) and (2,infinity) visual secret sharing by generalized random grids

► We have demonstrated the optimal contrast of any (2,n) GRG method. ► We have demonstrated the optimal contrast of any (2,infinity) GRG method. ► The proposed (2,n) and (2,infinity) GRG methods reach optimal contrast. Based on generalized random grids, this paper proposes two visual cryptography methods denoted as (2,n) GRG and (2,infinity) GRG. The (2,n) GRG is suitable for the pre-decided number of shares, and the (2,infinity) method is suitable for the adjustable number of shares. The proposed (2,n) GRG achieves better contrast on the stacking result, and the proposed (2,infinity) GRG enables extending the number of shares anytime. Based on the definition of contrast in Shyu’s work in 2007, we also demonstrate that the stacking result of (2,n) GRG is close to the theoretical bound of the contrast, and the stacking result of (2,infinity) GRG achieves the theoretical bound of the contrast.